Difference between revisions of "Excel to Analytica Mappings/Statistical Functions"

Revision as of 02:00, 6 January 2016

AVEDEV(x1, x2,...)

Analytica equivalents are Mean(x-Mean(x)) and Mean(x-Mean(x, I), I).

AVERAGE(x1, x2,...), AVERAGEA(x1, x2,...)

Analytica equivalent is Average(x, I).

AVERAGEA

AVERAGEIF

AVERAGEIFS

BETADIST(x, alpha, beta, A, B)

Analytica equivalents are BetaI(x, alpha, beta) and BetaI((x-A)/(B-A), alpha, beta).

To define a variable as a beta probability distribution, use:

Beta(alpha, beta, A, B)

BETA.DIST(x, alpha, beta, cumulative, A, B)

BETAINV(p, alpha, beta, A, B)

This is named BETA.INV(p, alpha, beta, A, B) in Excel 2010 , but the equivalent is the same.

Analytica equivalents are BetaIInv(p, alpha, beta) and BetaIInv(p, alpha, beta) * (B-A) + A.

To define a variable as a beta probability distribution, use:

Beta(alpha, beta, A, B)

BINOMDIST(x, n, p)

Analytica equivalent:

Prob_Binomial(x, n, p)

To use this function, add the Distribution Densities Library to your model.

To define a variable as binomially distributed, use:

Binomial(n, p)

For the cumulative binomial probability, BINOMDIST(x, n, p, TRUE), the Analytica equivalent is:

Probability(Binomial(n, p) <= x)

Note, however, that this is evaluated using sampling, so for small sample sizes there could be some sampling error in the result.

BINOM.DIST(number_s, trials, probability_s, cumulative)BINOM.INV(trials, probability_s, alpha)

The CumBinomialInv function found in the "Distribution Densities.ana" library starting with Analytica 4.4.3 provides the equivalent:

CumBinomialInv(alpha, trials, probability_s)CHIDIST(x, dof) or CHISQ.DIST(x, deg_freedom, cumulative)

Analytica equivalent for CHIDIST or CHISQ.DIST when cumulative is false:

Dens_ChiSquared(x, dof)

Equivalent of CHISQ.DIST when cumulative is true:

CumChiSquared(x, dof)

Both Dens_ChiSquared and CumChiSquared are in the Distribution Densities Library.

CHIINV(p,dof) or CHISQ.INV(p, dof)

Analytica equivalent:

2 * GammaIInv(p, dof/2)CHISQ.INV.RT(p, dof)CHITEST(actual,expected) or CHISQ.TEST(actual, expected)

For the 1-D case, where «actual» and «expected» are each 1-D, in Analytica these will have a common index, I, and the Analytica equivalent is:

Var n := Sum(1, I);
Var chi2 := Sum((actual-expected)^2 / expected, I);
1-GammaI(chi2/2, (n-1)/2)

For the 2-D contingency table analysis, with indexes I and J, the equivalent is:

Var n := Sum(1, I, J);
Var chi2 := Sum( (actual-expected)^2 / expected, I, J);
1-GammaI(chi2/2, (n-1)/2)

CONFIDENCE(alpha, sd, n) or CONFIDENCE.NORM(alpha, sd, n)

Analytica equivalent:

CumNormalInv(0.5 + (1-alpha)/2, 0, sd ) / Sqrt(n)CONFIDENCE.T(alpha, sd, n)

Analytica equivalent:

-CumStudentTInv(alpha/2, n-1)*sd/Sqrt(n)

Note: CumStudentTInv is in the Distribution Densities library.

CORREL(x, y)

Analytica equivalents are Correlation(x, y) and Correlation(x, y, I)
Use the first form, without the index, when measuring correlation across the Run index (e.g., the Monte Carlo uncertainty dimension).

COUNT(value1, value2,...), COUNTA(value1, value2,...)

Analytica equivalents, e.g.,:

Sum(IsNumber(x), I)
Sum(x <> Null, I)

COUNTBLANK

The notion of a blank Excel cell does not directly translate, but in Analytica we would generally consider a cell of an array to be blank when its value is null.  Thus, the Analytica equivalent would be:

Sum(x=null, I)

COUNTIF(range, criteria)

The Analytica equivalent consists of expressing criteria as a boolean expression and then using:

Sum(criteria,I)

For example, to count the number of values greater than 55, use:

Sum(range>55,I)

COUNTIFS(range1, criteria1, range2, critieria2, range3, criteria3,...)

Most cases where you would use this function in Excel involve collections of data that are logically 3 or 4 dimensional, but which have to be broken into multiple tables because of Excel's intrinsic restriction to two dimensions.  Hence, multiple ranges are naturally handled via array abstraction without a need for special handling.  
For example, in an array named range with 4 dimensions: I,J,K and L, to count the number of values greater than 55 you would use:

Sum(range>55,I,J,K,L)

If the criteria varies along one or more of the dimensions, then your criteria would simply be indexed by that.  For example, if you have separate bounds for each value along L, you would create an array, Lb, indexed by L and containing the lower bounds, and then use:

Sum(range>lb,I,J,K,L)

COVAR(array1, array2) or COVARIANCE.S(array1, array2)

Analytica equivalent:

CoVariance(array1,array2,I)

COVARIANCE.P(array1, array2)

Analytica equivalent:

Var n := Sum(1,I);
CoVariance(array1,array2,I) * (n-1) / n

CRITBINOM(alpha, trials, probability_s)

The CRITBINOM computes the inverse CDF for a binomial distribution.  The CumBinomialInv function found in the "Distribution Densities.ana" library starting with Analytica 4.4.3 provides the equivalent:

CumBinomialInv(alpha,trials,probability_s)DEVSQ(number1, number2,...)

Analytica equivalents:

Sum( (X-Mean(X,I))^2, I )
Variance(X,I) * (Sum(1,I)-1)

where the numbers are in array X indexed by I.

EXPONDIST(x, lambda, cumulative) or EXPON.DIST(x, lambda, cumulative)

If cumulative is false, the Analytica equivalent is:

Dens_Exponential(x,1/lambda)

When cumulative is true, the Analytica equivalent is:

CumExponential(x,1/lambda)

Note: These functions are in the Distribution Densities library

F.DIST(x, dof1, dof2, cumulative)

When cumulative is true, the Analytica equivalent is:

CumFDist(x, dof1, dof2)

When cumulative is false:

Dens_FDist(x, dof1, dof2)

Note: CumFDist and Dens_FDist are in the Distribution Densities library

FDIST(x, dof1, dof2) or F.DIST.RT(x, dof1, dof2)

The Analytica equivalent is

1-CumFDist(x,dof1,dof2)

Note: CumFDist is the Distribution Densities library

F.INV(p, dof1, dof2)

The Analytica equivalent is:

CumFDistInv(p, dof1, dof2)

FINV(p, dof1, dof2) or F.INV.RT(p, dof1, dof2)

The Analytica equivalent is:

CumFDistInv(1-p,dof1,dof2)

F.TEST(array1, array2)

The Analytica equivalent, assuming «array1» is indexed by I and «array2» is indexed by J is:

Var F0 := Variance(array1,I) / Variance(array2,J);
Var F  := Max([F0,1/F0]);
2 * (1-CumFDist(F,Sum(1,I)-1,Sum(1,J)-1) )

FISHER(x)

The Analytica equivalent is:

Ln( (1+x)/(1-x) ) / 2

FISHERINV(y)

The Analytica equivalent is:

Var e2y := Exp(2*y) Do (e2y-1)/(e2y+1)

FORECAST(x, known_y, known_x)

Analytica equivalent (Index I an the index in common with known_x and known_y):

Index K := ['b','m'];
Var B := Array(K,[1,known_x]);
Var Bx := Array(K,[1,x]);
Sum(Regression(known_y,B,I,K) * Bx, K )

FREQUENCY(data_array, bins_array)

Analytica equivalentd:

Frequency(data_array,bins_array)
Frequency(data_array,bins_array,I)

The second form is used when data_array is indexed by I.  The first form takes the frequency of the uncertain sample, i.e., along the Run index.

FTEST(array1, array2)

The following User-Defined Function provides an Analytica equivalent:

Function FTest( A1 : ContextSamp[I], A2 : ContextSamp[J] ; I,J : Index = Run )
Definition:
   Var v1 := Variance(A1,I);
   Var v2 := Variance(A2,J);
   Var n1 := Sum(1,I);
   Var n2 := Sum(1,J);
   Var F := v2/v1;
   1 - CumFDist(F,n1-1,n2-1)

Add the above UDF to your model, then you can just use:

FTest(array1,array2,I,J)

where I and J are the indexes of array1 and array2 respectively.

GAMMADIST(x, a, b, cumulative) or GAMMA.DIST(x, a, b, cumulative)

Analytica equivalent of GAMMADIST(x,a,b):

Dens_Gamma(x,a,b)

Analytica equivalent of GAMMADIST(x,a,b,TRUE):

GammaI(x,a,b)

To define a variable as uncertain with a gamma probability distribution, use:

Gamma(a,b)

Note: Dens_Gamma is in the Distribution Densities library

GAMMAINV(p, a, b) or GAMMA.INV(p, a, b)

Analytica equivalent:

GammaIInv(p,a,b)

GAMMALN(x)

Analytica equivalent:

LGamma(x)

GEOMEAN(x1, x2,...)

The Analytica equivalent is this statistical function:

Function GeoMean( x : ContextSamp[I] ; I : Index = Run )
Definition: Exp(Mean(Ln(x),I))

GROWTHHARMEAN(x1, x2,...)

Given an array x indexed by I, the Harmonic mean in Analytica is computed as:

Sum(1,I) / Sum(1/x,I)

HYPGEOMDIST(sample_s, number_sample, population_s, number_pop)

The Analytica equivalent is:

Prob_HyperGeometric(sample_s,number_sample,population,number_pop)

HYPGEOM.DIST(sample_s, number_sample, population_s, number_pop, cumulative)

When cumulative is false, the Analytica equivalent is:

Prob_HyperGeometric(sample_s,number_sample,population,number_pop)

When cumulative is true, the Analytica equivalent is:

Sum(Prob_HyperGeometric(0..sample_s,number_sample,population,number_pop))

INTERCEPT(known_y, known_x)

Assume known_y and known_x share index I.  The Analytica equivalent is:

Index K := ['b','m'];
Regression( known_y, Array(K,[1,known_x]), I, K ) [ K='b' ]

KURT(number1, number2,...)

Analytica equivalents:

Kurtosis(X)
Kurtosis(X,I)

LARGE(array, k)

Assume array is indexed by I.   One possible Analytica equivalent is:

Var n := Sum(1,I);
X[I=ArgMax(Rank(array,I)=n+1-k,I)]

LINESTLOGESTLOGINV(p, lm, lsd)

The Analytica equivalent is:

CumLogNormalInv(p,Exp(lm),Exp(lsd))

LOGNORMDIST(x, lm, ls)

The Analytica equivalent is:

CumLogNormal(x,Exp(lm),Exp(ls))

LOGNORM.DIST(x, lm, ls, cumulative)

When cumulative is true, the Analytica equivalent is

CumLogNormal(x,Exp(lm),Exp(ls))

When cumulative is false, the Analytica equivalent is

Dens_LogNormal(x,Exp(lm),Exp(ls))

Note: Dens_LogNormal and CumLogNormal are in the Distribution Densities library.

LOGNORM.INV(p, lm, ls)

The Analytica equivalent is:

CumLogNormalInv(p,Exp(lm),Exp(ls))

Note: CumLogNormalInv is in the Distribution Densities library.

MAX(number1, number2,...) or MAXA(number1, number2,...)

When MAX is applied in Excel to individual numbers, the Analytica equivalent is:

Max( [number1,number2,...] )

Take note of the square brackets.
When MAX is used in Excel by providing it with a range of cells, the Analytica equivalent is

Max(A,I)

where A is the array of values (analogous to Excel's range) and I is the index to take the max over.  In the two-D case, where you want the Max over a 2-D region, this becomes:

Max(A,I,J)

In Excel, MAX ignores text (non-numbers) while MAXA does not.  To ignore non-numbers, use the optional ignoreNonNumbers parameter:

Max(A,I,ignoreNonNumbers: true)

MEDIAN(number1, number2,...)

When MEDIAN is applied in Excel to individual numbers, the Analytica equivalent is:

Index x := [number1,number2,...];
GetFract( x,0.5,x )

In the more usual case, when MEDIAN is used in Excel by providing it with a range of cells, the Analytica equivalent is

GetFract(A,0.5,I)

where A is the array of values (analogous to Excel's range) and I is the index to take the median over.

MIN(number1, number2,...) and MINA(number1, number2,...)

When MIN or MINA is applied in Excel to individual numbers, the Analytica equivalent is:

Min( [number1,number2,...] )

Take note of the square brackets.
When MIN or MINA is used in Excel by providing it with a range of cells, the Analytica equivalent is

Min(A,I)

where A is the array of values (analogous to Excel's range) and I is the index to take the minimum over.  In the two-D case, where you want the minimum over a 2-D region, this becomes:

Min(A,I,J)

In Excel, MIN ignores text and non-numbers, while MINA does not.  To ignore text, etc., use the optional ignoreNonNumbers parameter:

Min(A,I,ignoreNonNumbers:true)

MODE(range)

Assuming the values in Analytica are in an array A indexed by I, the equivalent is:

Index V := Unique(Va1,Va1);
ArgMax(Frequency( Va1, V, Va1 ),V)

MODE.MULT(x1, x2,...)MODE.SNGL(x1, x2,...)NEGBINOMDISTNORMDIST(x, mean, standard_dev, cumulative)

If Cumulative=True, the Analytica equivalent is:

CumNormal(x,mean,standard_dev)

If Cumulative=False, the Analytica equivalent is:

Dens_Normal(x,mean,standard_dev)

Note that to use Dens_Normal, you must include the distribution densities library in your model.

NORMINV(p, mean, standard_dev)

Analytica equivalent:

CumNormalInv(p,mean,standard_dev)

NORMSDIST(z)

Analytica equivalent:

CumNormal(z)

NORMSINV(p)

Analytica equivalent:

 CumNormalInv(p)

PEARSON(array1, array2)

Analytica equivalent:

Correlation(array1,array2,I)

where the data points in array1 and array2 both are indexed by I.

PERCENTILE(array, p)

Assume that the array of values is indexed by I.  Then the Analytica equivalent is:

GetFract(array,p,I)

PERCENTRANK(array, x, significance)

Returns the rank of a value in a data set as a percentage of the data set.  The optional parameters, significance, defaults to 3 in Excel.  Assume your array is A and is indexed by I.  If you want the percent rank for all elements of A to full precision use:

(Rank(A,I)-1) / (Size(I)-1)

If you want the percent rank for all elements, but only to the indicated significance, use:

Floor( (Rank(A,I)-1) / (Size(I)-1), significance )

If you want to get the percent rank of a single element, use:

Floor( Sum(A<x,I) / (Size(I)-1), significance )

PERMUT(n, k)

Analytica equivalent:

Permutations(n,k)

POISSON(x, mean, cumulative)

When cumulative is false, the Analytica equivalent is

Prob_Poisson(x,mean)

When cumulative is true, the Analytica equivalent is

CumPoisson(x,mean)

In Analytica models, you'll often use the Poisson distribution function directly, rather than evaluating the probability or cumulative probability at a given point.

PROB(x_range, prob_range, lower_limit, upper_limit)

In Analytica, x_range and prob_range will share an index, call it I.  When upper_limit is not specified, then the Analytica equivalent is:

Sum( prob_range * (lower_limit <= x_range ), I )

When upper_limit is specified, this becomes

Sum( prob_range * (lower_limit <= x_range and x_range <= upper_limit), I )

QUARTILE(array, quart)

Analytica equivalent, where array is assumed indexed by I:

GetFract(array,quart/4,I)

RANK(number, range, order)

Assume in Analytica that the array identified by range is indexed by I.  Then when order is non-zero, the Analytica equivalent is:

Rank(range,I,type:-1)[I=number]

When order is omitted or zero in Excel, the Analytica equivalent is:

Rank(-range,I,type:1)[I=number]

RSQ(known_y,known_x)

Analytica equivalent:

Correlation(known_y,known_x,I)^2

SKEW(number1,number2,...)

Analytica equivalent (assume the numbers are in array X, indexed by I):

Skewness(X,I)

When X is an uncertain distribution, indexed by Run, the equivalent is:

Skewness(X)

SLOPE(known_y, known_x)

Assume known_y and known_x share index I.  The Analytica equivalent is:

Index K := ['b','m'];
Regression( known_y, Array(K,[1,known_x]), I, K ) [ K='m' ]

SMALL(array, k)

Assume array is indexed by I.   One possible Analytica equivalent is:

X[I=ArgMax(Rank(array,I)=k,I)]

STANDARDIZE(x, m, sd)

Analytica equivalent:

(x-m)/sd

STDEV(number1, number2,...)

Analytica equivalent (assume that the numbers are in array X indexed by I):

SDeviation(X,I)

STDEVP

Analytica equivalent (assume that the numbers are in array X indexed by I):

SDeviation(X,I) * (Sum(1,I)-1)/Sum(1,I)

STEYX(known_ys, known_xs)

To express the Analytica equivalent, I recommend first introducting an index and a function to your model:

Index Bm := ['b','m']
Function Basis_Bm(x) := Table(Bm)(1,x)

These functions make simple y=m*x+b linear regression very convenient.  With these, the equivalent is, assuming the common index between known_ys and known_xs is I:

Var c := Regression(known_ys,Basis_Bm(known_xs),I,Bm);
known_ys - Sum( c * Basis_Bm(known_xs), Bm )

TDIST(x, dof, tails)

The Analytica equivalent is:

tails * (1-CumStudentT(x,dof))

TINV(p, dof)

Analytica equivalent:

CumStudentTInv( 1-p/2, dof )

Excel has a strange notion of a 2-tailed Student-T distribution, which basically multiplies the probability by 2.  See its TDIST function.  TINV seems to do the inverse of this 2-tailed case, which leads to this strange equivalence.

TREND(known_y, known_x, new_x, const)

Assume that the data in known_y and known_x are indexed by index I, and the points in new_x are indexed by J.  Also assume that const is 0 (false) for a y=m*x+b curve, and 1 (true) for a y=m*b fit.  Then the Analytica equivalent is:

Index K := ['b','m'];
Sum( Regression(known_y,Array(K,[not const,known_x]),I,K) * Array(K,[not const,new_x]), K )

The result is the set of predicted new_y values, indexed by J.

TRIMMEAN(array, percent)

Assume the array is indexed by I.  The Analytica equivalent is

Var n := Sum(1,I);
Mean( A[I=SortIndex(A,I)], I, w:@I > percent*n/2 and @I < n+1-(percent*n/2) )

TTESTVAR(number1, number2,...)

Analytica equivalent (assume numbers are in array X indexed by I):

Variance(X,I)

VARP

Analytica equivalent (assume numbers are in array X indexed by I):

Variance(X,I) * (Sum(1,I)-1)/Sum(1,I)

WEIBULL(x, alpha, beta, cumulative)

When cumulative=false, the Analytica equivalent is:

Dens_Weibull(x,alpha,beta)

When cumulative=true, the Analytica equivalent is:

CumWeibull(x,alpha,beta)

ZTESTSee Also

@@ Line 1: / Line 1: @@
-= AVEDEV(x1'',x2,...'') =
+<div style="column-count:3;-moz-column-count:3;-webkit-column-count:3">
+__TOC__
+</div>
-Analytica equivalents:
+== AVEDEV(x1'', x2,...'') ==
- [[Mean]](x-[[Mean]](x))
- [[Mean]](x-[[Mean]](x,I),I)
+Analytica equivalents are [[Mean]](x-[[Mean]](x)) and [[Mean]](x-[[Mean]](x, I), I).
-= AVERAGE(x1'',x2,...''), AVERAGEA(x1'',x2,...'') =
+== AVERAGE(x1'', x2,...''), AVERAGEA(x1'', x2,...'') ==
-Analytica equivalent:
+Analytica equivalent is [[Average]](x, I).
- [[Average]](x,I)
-= AVERAGEA=
+== AVERAGEA==
-= AVERAGEIF =
+== AVERAGEIF ==
-= AVERAGEIFS =
+== AVERAGEIFS ==
-= BETADIST(x,alpha,beta'',A,B'') =
+== BETADIST(x, alpha, beta'', A, B'') ==
-Analytica equivalents:
+Analytica equivalents are [[BetaI]](x, alpha, beta) and [[BetaI]]((x-A)/(B-A), alpha, beta).
- [[BetaI]](x,alpha,beta)
- [[BetaI]]((x-A)/(B-A),alpha,beta)
 To define a variable as a beta probability distribution, use:
- [[Beta]](alpha,beta'',A,B'')
+:<code>Beta(alpha, beta'', A, B'')</code>
-= BETA.DIST(x,alpha,beta,cumulative'',A,B'') =
+== BETA.DIST(x, alpha, beta, cumulative'', A, B'') ==
-= BETAINV(p,alpha,beta'',A,B'') =
+== BETAINV(p, alpha, beta'', A, B'') ==
-:''This is named ''BETA.INV(p,alpha,beta,A,B)'' in Excel 2010 ,but the equivalent is the same.
+This is named <code>BETA.INV(p, alpha, beta, A, B)</code> in Excel 2010 , but the equivalent is the same.
-Analytica equivalents:
+Analytica equivalents are [[BetaIInv]](p, alpha, beta) and [[BetaIInv]](p, alpha, beta) * (B-A) + A.
- [[BetaIInv]](p,alpha,beta)
- [[BetaIInv]](p,alpha,beta) * (B-A) + A
 To define a variable as a beta probability distribution, use:
- [[Beta]](alpha,beta'',A,B'')
+:<code>Beta(alpha, beta'', A, B'')</code>
-= BINOMDIST(x,n,p) =
+== BINOMDIST(x, n, p) ==
 Analytica equivalent:
- [[Prob_Binomial]](x,n,p)
+:<code>Prob_Binomial(x, n, p)</code>
 To use this function, add the Distribution Densities Library to your model.
 To define a variable as binomially distributed, use:
- [[Binomial]](n,p)
+:<code>Binomial(n, p)</code>
-For the cumulative binomial probability, BINOMDIST(x,n,p,TRUE), the Analytica equivalent is:
+For the cumulative binomial probability, <code>BINOMDIST(x, n, p, TRUE)</code>, the Analytica equivalent is:
- [[Probability]]([[Binomial]](n,p)<=x)
+:<code>Probability(Binomial(n, p) <= x)
 Note, however, that this is evaluated using sampling, so for small sample sizes there could be some sampling error in the result.
-= BINOM.DIST(number_s,trials,probability_s,cumulative) =
+== BINOM.DIST(number_s, trials, probability_s, cumulative) ==
-= BINOM.INV(trials,probability_s,alpha) =
+== BINOM.INV(trials, probability_s, alpha) ==
 The [[CumBinomialInv]] function found in the <code>"Distribution Densities.ana"</code> library starting with Analytica 4.4.3 provides the equivalent:
-:<code>CumBinomialInv(alpha,trials,probability_s)</code>
+:<code>CumBinomialInv(alpha, trials, probability_s)</code>
-= CHIDIST(x,dof) or CHISQ.DIST(x,deg_freedom,cumulative) =
+== CHIDIST(x, dof) or CHISQ.DIST(x, deg_freedom, cumulative) ==
 Analytica equivalent for CHIDIST or CHISQ.DIST when cumulative is false:
- [[Dens_ChiSquared]](x,dof)
+:<code>Dens_ChiSquared(x, dof)</code>
 Equivalent of CHISQ.DIST when cumulative is true:
- [[CumChiSquared]](x,dof)
+:<code>CumChiSquared(x, dof)</code>
 Both [[Dens_ChiSquared]] and [[CumChiSquared]] are in the <code>Distribution Densities Library</code>.
-= CHIINV(p,dof) or CHISQ.INV(p,dof) =
+== CHIINV(p,dof) or CHISQ.INV(p, dof) ==
 Analytica equivalent:
-* [[GammaIInv]](p,dof/2)
+:<code>2 * [[GammaIInv]](p, dof/2)</code>
-= CHISQ.INV.RT(p,dof) =
+== CHISQ.INV.RT(p, dof) ==
-= CHITEST(actual,expected) or CHISQ.TEST(actual,expected) =
+== CHITEST(actual,expected) or CHISQ.TEST(actual, expected) ==
-For the 1-D case, where ''actual'' and ''expected'' are each 1-D, in Analytica these will have a common index, I, and the Analytica equivalent is:
+For the 1-D case, where «actual» and «expected» are each 1-D, in Analytica these will have a common index, <code>I</code>, and the Analytica equivalent is:
- Var n := [[Sum]](1,I);
+:<code>Var n := Sum(1, I);</code>
- Var chi2 := [[Sum]]( (actual-expected)^2 / expected, I );
+:<code>Var chi2 := Sum((actual-expected)^2 / expected, I);</code>
--[[GammaI]](chi2/2,(n-1)/2)
+:<code>1-GammaI(chi2/2, (n-1)/2)</code>
-For the 2-D contingency table analysis, with indexes I and J, the equivalent is:
+For the 2-D contingency table analysis, with indexes <code>I</code> and <code>J</code>, the equivalent is:
- Var n := [[Sum]](1,I,J);
+:<code>Var n := Sum(1, I, J);</code>
- Var chi2 := [[Sum]]( (actual-expected)^2 / expected, I, J );
+:<code>Var chi2 := Sum( (actual-expected)^2 / expected, I, J);</code>
--[[GammaI]](chi2/2,(n-1)/2)
+:<code>1-GammaI(chi2/2, (n-1)/2)</code>
-= CONFIDENCE(alpha,sd,n) or CONFIDENCE.NORM(alpha,sd,n) =
+== CONFIDENCE(alpha, sd, n) or CONFIDENCE.NORM(alpha, sd, n) ==
 Analytica equivalent:
- [[CumNormalInv]]( 0.5 + (1-alpha)/2, 0, sd ) / [[Sqrt]](n)
+:<code>CumNormalInv(0.5 + (1-alpha)/2, 0, sd ) / Sqrt(n)</code>
-= CONFIDENCE.T(alpha,sd,n) =
+== CONFIDENCE.T(alpha, sd, n) ==
 Analytica equivalent:
- -[[CumStudentTInv]](alpha/2,n-1) * sd / [[Sqrt]](n)
+:<code>-CumStudentTInv(alpha/2, n-1)*sd/Sqrt(n)</code>
 ''Note: [[CumStudentTInv]] is in the <code>Distribution Densities</code> library.''
-= CORREL(x,y) =
+== CORREL(x, y) ==
-Analytica equivalents:
+Analytica equivalents are [[Correlation]](x, y) and [[Correlation]](x, y, I)
- [[Correlation]](x,y)
- [[Correlation]](x,y,I)
 Use the first form, without the index, when measuring correlation across the [[Run]] index (e.g., the Monte Carlo uncertainty dimension).
-= COUNT(value1'',value2,...''), COUNTA(value1'',value2,...'') =
+== COUNT(value1'', value2,...''), COUNTA(value1'', value2,...'') ==
 Analytica equivalents, e.g.,:
-  [[Sum]]( IsNumber(x), I )
+  [[Sum]](IsNumber(x), I)
-  [[Sum]]( x<>Null, I )
+  [[Sum]](x <> Null, I)
-= COUNTBLANK =
+== COUNTBLANK ==
 The notion of a blank Excel cell does not directly translate, but in Analytica we would generally consider a cell of an array to be blank when its value is null.  Thus, the Analytica equivalent would be:
-  [[Sum]]( x=null, I )
+  [[Sum]](x=null, I)
-= COUNTIF(range,criteria) =
+== COUNTIF(range, criteria) ==
 The Analytica equivalent consists of expressing criteria as a boolean expression and then using:
@@ Line 128: / Line 123: @@
   [[Sum]](range>55,I)
-= COUNTIFS(range1,criteria1'',range2,critieria2,range3,criteria3,...'') =
+== COUNTIFS(range1, criteria1'', range2, critieria2, range3, criteria3,...'') ==
 Most cases where you would use this function in Excel involve collections of data that are logically 3 or 4 dimensional, but which have to be broken into multiple tables because of Excel's intrinsic restriction to two dimensions.  Hence, multiple ranges are naturally handled via array abstraction without a need for special handling.
@@ Line 140: / Line 135: @@
   [[Sum]](range>lb,I,J,K,L)
-= COVAR(array1,array2) or COVARIANCE.S(array1,array2) =
+== COVAR(array1, array2) or COVARIANCE.S(array1, array2) ==
 Analytica equivalent:
   [[CoVariance]](array1,array2,I)
-= COVARIANCE.P(array1,array2) =
+== COVARIANCE.P(array1, array2) ==
 Analytica equivalent:
@@ Line 152: / Line 147: @@
   [[CoVariance]](array1,array2,I) * (n-1) / n
-= CRITBINOM(alpha,trials,probability_s) =
+== CRITBINOM(alpha, trials, probability_s) ==
 The CRITBINOM computes the inverse CDF for a binomial distribution.  The [[CumBinomialInv]] function found in the <code>"Distribution Densities.ana"</code> library starting with Analytica 4.4.3 provides the equivalent:
 :<code>CumBinomialInv(alpha,trials,probability_s)</code>
-= DEVSQ(number1'',number2,...'') =
+== DEVSQ(number1'', number2,...'') ==
 Analytica equivalents:
@@ Line 165: / Line 160: @@
 where the numbers are in array ''X'' indexed by ''I''.
-= EXPONDIST(x,lambda'',cumulative'') or EXPON.DIST(x,lambda'',cumulative'')=
+== EXPONDIST(x, lambda'', cumulative'') or EXPON.DIST(x, lambda'', cumulative'')==
 If cumulative is false, the Analytica equivalent is:
@@ Line 175: / Line 170: @@
 ''Note: These functions are in the '''Distribution Densities''' library''
-= F.DIST(x,dof1,dof2,cumulative) =
+== F.DIST(x, dof1, dof2, cumulative) ==
 When ''cumulative'' is true, the Analytica equivalent is:
-  [[CumFDist]](x,dof1,dof2)
+  [[CumFDist]](x, dof1, dof2)
 When ''cumulative'' is false:
-  [[Dens_FDist]](x,dof1,dof2)
+  [[Dens_FDist]](x, dof1, dof2)
 ''Note: [[CumFDist]] and [[Dens_FDist]] are in the '''Distribution Densities''' library''
-= FDIST(x,dof1,dof2) or F.DIST.RT(x,dof1,dof2) =
+== FDIST(x, dof1, dof2) or F.DIST.RT(x, dof1, dof2) ==
 The Analytica equivalent is
@@ Line 192: / Line 187: @@
 ''Note: [[CumFDist]] is the '''Distribution Densities''' library''
-= F.INV(p,dof1,dof2) =
+== F.INV(p, dof1, dof2) ==
 The Analytica equivalent is:
-  [[CumFDistInv]](p,dof1,dof2)
+  [[CumFDistInv]](p, dof1, dof2)
-= FINV(p,dof1,dof2) or F.INV.RT(p,dof1,dof2) =
+== FINV(p, dof1, dof2) or F.INV.RT(p, dof1, dof2) ==
 The Analytica equivalent is:
   [[CumFDistInv]](1-p,dof1,dof2)
-= F.TEST(array1,array2) =
+== F.TEST(array1, array2) ==
 The Analytica equivalent, assuming «array1» is indexed by ''I'' and «array2» is indexed by ''J'' is:
@@ Line 210: / Line 205: @@
 * (1-[[CumFDist]](F,[[Sum]](1,I)-1,[[Sum]](1,J)-1) )
-= FISHER(x) =
+== FISHER(x) ==
 The Analytica equivalent is:
@@ Line 216: / Line 211: @@
   [[Ln]]( (1+x)/(1-x) ) / 2
-= FISHERINV(y) =
+== FISHERINV(y) ==
 The Analytica equivalent is:
   [[Var]] e2y := [[Exp]](2*y) Do (e2y-1)/(e2y+1)
-= FORECAST(x,known_y,known_x) =
+== FORECAST(x, known_y, known_x) ==
 Analytica equivalent (Index I an the index in common with ''known_x'' and ''known_y''):
@@ Line 229: / Line 224: @@
   [[Sum]]([[Regression]](known_y,B,I,K) * Bx, K )
-= FREQUENCY(data_array,bins_array) =
+== FREQUENCY(data_array, bins_array) ==
 Analytica equivalentd:
@@ Line 237: / Line 232: @@
 The second form is used when data_array is indexed by I.  The first form takes the frequency of the uncertain sample, i.e., along the [[Run]] index.
-= FTEST(array1,array2) =
+== FTEST(array1, array2) ==
 The following [[User-Defined Function]] provides an Analytica equivalent:
@@ Line 253: / Line 248: @@
 where ''I'' and ''J'' are the indexes of ''array1'' and ''array2'' respectively.
-= GAMMADIST(x,a,b'',cumulative'') or GAMMA.DIST(x,a,b,cumulative) =
+== GAMMADIST(x, a, b'', cumulative'') or GAMMA.DIST(x, a, b, cumulative) ==
 Analytica equivalent of GAMMADIST(x,a,b):
@@ Line 266: / Line 261: @@
 ''Note: [[Dens_Gamma]] is in the '''Distribution Densities''' library''
-= GAMMAINV(p,a,b) or GAMMA.INV(p,a,b) =
+== GAMMAINV(p, a, b) or GAMMA.INV(p, a, b) ==
 Analytica equivalent:
   [[GammaIInv]](p,a,b)
-= GAMMALN(x) =
+== GAMMALN(x) ==
 Analytica equivalent:
   [[LGamma]](x)
-= GEOMEAN(x1,x2,...) =
+== GEOMEAN(x1, x2,...) ==
 The Analytica equivalent is this [[Statistical Functions and Importance Weighting|statistical function]]:
@@ Line 282: / Line 277: @@
   Definition: [[Exp]]([[Mean]]([[Ln]](x),I))
-= GROWTH =
+== GROWTH ==
-= HARMEAN(x1'',x2,...'') =
+== HARMEAN(x1'', x2,...'') ==
 Given an array ''x'' indexed by I, the Harmonic mean in Analytica is computed as:
   [[Sum]](1,I) / [[Sum]](1/x,I)
-= HYPGEOMDIST(sample_s,number_sample,population_s,number_pop) =
+== HYPGEOMDIST(sample_s, number_sample, population_s, number_pop) ==
 The Analytica equivalent is:
   [[Prob_HyperGeometric]](sample_s,number_sample,population,number_pop)
-= HYPGEOM.DIST(sample_s,number_sample,population_s,number_pop,cumulative) =
+== HYPGEOM.DIST(sample_s, number_sample, population_s, number_pop, cumulative) ==
 When ''cumulative'' is false, the Analytica equivalent is:
@@ Line 301: / Line 296: @@
   [[Sum]]([[Prob_HyperGeometric]](0..sample_s,number_sample,population,number_pop))
-= INTERCEPT(known_y,known_x) =
+== INTERCEPT(known_y, known_x) ==
 Assume ''known_y'' and ''known_x'' share index ''I''.  The Analytica equivalent is:
@@ Line 307: / Line 302: @@
   Regression( known_y, Array(K,[1,known_x]), I, K ) [ K='b' ]
-= KURT(number1'',number2,...'') =
+== KURT(number1'', number2,...'') ==
 Analytica equivalents:
@@ Line 313: / Line 308: @@
   [[Kurtosis]](X,I)
-= LARGE(array,k) =
+== LARGE(array, k) ==
 Assume ''array'' is indexed by I.   One possible Analytica equivalent is:
@@ Line 319: / Line 314: @@
   X[I=[[ArgMax]]([[Rank]](array,I)=n+1-k,I)]
-= LINEST =
+== LINEST ==
-= LOGEST =
+== LOGEST ==
-= LOGINV(p,lm,lsd) =
+== LOGINV(p, lm, lsd) ==
 The Analytica equivalent is:
   [[CumLogNormalInv]](p,[[Exp]](lm),[[Exp]](lsd))
-= LOGNORMDIST(x,lm,ls) =
+== LOGNORMDIST(x, lm, ls) ==
 The Analytica equivalent is:
   [[CumLogNormal]](x,[[Exp]](lm),[[Exp]](ls))
-= LOGNORM.DIST(x,lm,ls,cumulative) =
+== LOGNORM.DIST(x, lm, ls, cumulative) ==
 When ''cumulative'' is true, the Analytica equivalent is
@@ Line 341: / Line 336: @@
 ''Note: [[Dens_LogNormal]] and [[CumLogNormal]] are in the '''Distribution Densities''' library''.
-= LOGNORM.INV(p,lm,ls) =
+== LOGNORM.INV(p, lm,  ls) ==
 The Analytica equivalent is:
@@ Line 348: / Line 343: @@
 ''Note: [[CumLogNormalInv]] is in the '''Distribution Densities''' library''.
-= MAX(number1'',number2,...'') or MAXA(number1'',number2,...'')=
+== MAX(number1'', number2,...'') or MAXA(number1'', number2,...'')==
 When MAX is applied in Excel to individual numbers, the Analytica equivalent is:
@@ Line 360: / Line 355: @@
 In Excel, MAX ignores text (non-numbers) while MAXA does not.  To ignore non-numbers, use the optional ''ignoreNonNumbers'' parameter:
-  [[Max]](A,I,ignoreNonNumbers:true)
+  [[Max]](A,I,ignoreNonNumbers: true)
-= MEDIAN(number1'',number2,...'') =
+== MEDIAN(number1'', number2,...'') ==
 When MEDIAN is applied in Excel to individual numbers, the Analytica equivalent is:
@@ Line 372: / Line 367: @@
 where ''A'' is the array of values (analogous to Excel's range) and I is the index to take the median over.
-= MIN(number1'',number2,...'') and MINA(number1'',number2,...'') =
+== MIN(number1'', number2,...'') and MINA(number1'', number2,...'') ==
 When MIN or MINA is applied in Excel to individual numbers, the Analytica equivalent is:
@@ Line 386: / Line 381: @@
   [[Min]](A,I,ignoreNonNumbers:true)
-= MODE(range) =
+== MODE(range) ==
 Assuming the values in Analytica are in an array ''A'' indexed by ''I'', the equivalent is:
@@ Line 393: / Line 388: @@
   [[ArgMax]]([[Frequency]]( Va1, V, Va1 ),V)
-= MODE.MULT(x1'',x2,...'') =
+== MODE.MULT(x1'', x2,...'') ==
-= MODE.SNGL(x1'',x2,...'') =
+== MODE.SNGL(x1'', x2,...'') ==
-= NEGBINOMDIST =
+== NEGBINOMDIST ==
-= NORMDIST(x,mean,standard_dev'',cumulative'') =
+== NORMDIST(x, mean, standard_dev'', cumulative'') ==
 If ''Cumulative''=True, the Analytica equivalent is:
@@ Line 408: / Line 403: @@
 Note that to use [[Dens_Normal]], you must include the distribution densities library in your model.
-= NORMINV(p,mean,standard_dev) =
+== NORMINV(p, mean, standard_dev) ==
 Analytica equivalent:
   [[CumNormalInv]](p,mean,standard_dev)
-= NORMSDIST(z) =
+== NORMSDIST(z) ==
 Analytica equivalent:
   [[CumNormal]](z)
-= NORMSINV(p) =
+== NORMSINV(p) ==
 Analytica equivalent:
    [[CumNormalInv]](p)
-= PEARSON(array1,array2) =
+== PEARSON(array1, array2) ==
 Analytica equivalent:
@@ Line 430: / Line 425: @@
-= PERCENTILE(array,p) =
+== PERCENTILE(array, p) ==
 Assume that the array of values is indexed by I.  Then the Analytica equivalent is:
   [[GetFract]](array,p,I)
-= PERCENTRANK(array,x'',significance'') =
+== PERCENTRANK(array, x'', significance'') ==
 Returns the rank of a value in a data set as a percentage of the data set.  The optional parameters, ''significance'', defaults to 3 in Excel.  Assume your array is ''A'' and is indexed by ''I''.  If you want the percent rank for all elements of A to full precision use:
@@ Line 449: / Line 444: @@
   [[Floor]]( [[Sum]](A<x,I) / ([[Size]](I)-1), significance )
-= PERMUT(n,k) =
+== PERMUT(n, k) ==
 Analytica equivalent:
   [[Permutations]](n,k)
-= POISSON(x,mean,cumulative) =
+== POISSON(x, mean, cumulative) ==
 When ''cumulative'' is ''false'', the Analytica equivalent is
@@ Line 464: / Line 459: @@
 In Analytica models, you'll often use the [[Poisson]] distribution function directly, rather than evaluating the probability or cumulative probability at a given point.
-= PROB(x_range,prob_range,lower_limit'',upper_limit'') =
+== PROB(x_range, prob_range, lower_limit'', upper_limit'') ==
 In Analytica, ''x_range'' and ''prob_range'' will share an index, call it ''I''.  When ''upper_limit'' is not specified, then the Analytica equivalent is:
@@ Line 472: / Line 467: @@
   [[Sum]]( prob_range * (lower_limit <= x_range and x_range <= upper_limit), I )
-= QUARTILE(array,quart) =
+== QUARTILE(array, quart) ==
 Analytica equivalent, where ''array'' is assumed indexed by ''I'':
   [[GetFract]](array,quart/4,I)
-= RANK(number,range'',order'') =
+== RANK(number, range'', order'') ==
 Assume in Analytica that the array identified by ''range'' is indexed by ''I''.  Then when ''order'' is non-zero, the Analytica equivalent is:
@@ Line 485: / Line 480: @@
   [[Rank]](-range,I,type:1)[I=number]
-= RSQ(known_y,known_x) =
+== RSQ(known_y,known_x) ==
 Analytica equivalent:
   [[Correlation]](known_y,known_x,I)^2
-= SKEW(number1'',number2,...'') =
+== SKEW(number1'',number2,...'') ==
 Analytica equivalent (assume the numbers are in array ''X'', indexed by ''I''):
@@ Line 498: / Line 493: @@
   [[Skewness]](X)
-= SLOPE(known_y,known_x) =
+== SLOPE(known_y, known_x) ==
 Assume ''known_y'' and ''known_x'' share index ''I''.  The Analytica equivalent is:
@@ Line 505: / Line 500: @@
-= SMALL(array,k) =
+== SMALL(array, k) ==
 Assume ''array'' is indexed by I.   One possible Analytica equivalent is:
@@ Line 511: / Line 506: @@
-= STANDARDIZE(x,m,sd) =
+== STANDARDIZE(x, m, sd) ==
 Analytica equivalent:
   (x-m)/sd
-= STDEV(number1'',number2,...'') =
+== STDEV(number1'', number2,...'') ==
 Analytica equivalent (assume that the numbers are in array ''X'' indexed by ''I''):
   [[SDeviation]](X,I)
-= STDEVP =
+== STDEVP ==
 Analytica equivalent (assume that the numbers are in array ''X'' indexed by ''I''):
   [[SDeviation]](X,I) * ([[Sum]](1,I)-1)/[[Sum]](1,I)
-= STEYX(known_ys,known_xs) =
+== STEYX(known_ys, known_xs) ==
 To express the Analytica equivalent, I recommend first introducting an index and a function to your model:
@@ Line 537: / Line 532: @@
   known_ys - [[Sum]]( c * Basis_Bm(known_xs), Bm )
-= TDIST(x,dof,tails) =
+== TDIST(x, dof, tails) ==
 The Analytica equivalent is:
   tails * (1-[[CumStudentT]](x,dof))
-= TINV(p,dof) =
+== TINV(p, dof) ==
 Analytica equivalent:
@@ Line 549: / Line 544: @@
 Excel has a strange notion of a 2-tailed Student-T distribution, which basically multiplies the probability by 2.  See its TDIST function.  TINV seems to do the inverse of this 2-tailed case, which leads to this strange equivalence.
-= TREND(known_y'',known_x,new_x,const'') =
+== TREND(known_y'', known_x, new_x, const'') ==
 Assume that the data in ''known_y'' and ''known_x'' are indexed by index ''I'', and the points in ''new_x'' are indexed by ''J''.  Also assume that const is 0 (false) for a ''y=m*x+b'' curve, and 1 (true) for a ''y=m*b'' fit.  Then the Analytica equivalent is:
@@ Line 557: / Line 552: @@
 The result is the set of predicted ''new_y'' values, indexed by ''J''.
-= TRIMMEAN(array,percent) =
+== TRIMMEAN(array, percent) ==
 Assume the array is indexed by ''I''.  The Analytica equivalent is
@@ Line 563: / Line 558: @@
   [[Mean]]( A[I=[[SortIndex]](A,I)], I, w:@I > percent*n/2 and @I < n+1-(percent*n/2) )
-= TTEST =
+== TTEST ==
-= VAR(number1'',number2,...'') =
+== VAR(number1'', number2,...'') ==
 Analytica equivalent (assume numbers are in array X indexed by I):
   [[Variance]](X,I)
-= VARP =
+== VARP ==
 Analytica equivalent (assume numbers are in array X indexed by I):
@@ Line 575: / Line 570: @@
-= WEIBULL(x,alpha,beta,cumulative) =
+== WEIBULL(x, alpha, beta, cumulative) ==
 When ''cumulative=false'', the Analytica equivalent is:
@@ Line 583: / Line 578: @@
   [[CumWeibull]](x,alpha,beta)
-= ZTEST =
+== ZTEST ==
+==See Also==